356 On the Attraction of Ellipsoids. 



Let cos = u, this expression becomes 



Jo 



obc u 2 du 





+ W 2 (fl 2 -C 2 )} v/{c 2 + W 2 (i 2 -C 2 )}' 



In the same way it may be shown that the attraction of the 

 ellipsoid on a point /m placed at the extremity of the mean 

 axis is 



abc u 2 du 



+ u 2 (c 2 - b 2 )} ^{b 2 + u 2 (a 2 -b 2 )}' 

 and on a point at the extremity of the greatest axis, 



A j. f 1 abcu 2 du 



^WP ,i 2 r/Ii zvi 77~* T7~2 2TT- 



J o */ \a 2 + u 2 (b 2 - a 2 ) } -y/ (a 3 + u 2 (c 2 - a 2 ) } 



It will be seen in a subsequent proposition, that these three 

 expressions are not independent of each other, the values of the 

 three attractions in question being connected by an equation. 



PROPOSITION III. 



To give Geometrical Representations of the Attraction of an 

 Ellipsoid on Points placed at the extremities of its least and mean 

 Axes* 



Fig. 3. 



On the greater axis OA of the focal ellipse assume a point 

 such that OKi = - OA ; from the point Kj draw a tangent 



C 



* Proceedings of the Koyal Irish Academy, VOL. in. p. 367. 



